An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Abstract

Abstract:To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger's equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.